This invention relates to crystal resonators manufactured to control their acceleration sensitivity.
Piezoelectric quartz crystal resonators are used to develop highly accurate timing signals and reference frequencies for such applications as communications, navigation and radar. In particular, resonant frequencies of thickness shear mode quartz resonators are commonly used as timing standards in crystal-controlled oscillators.
In spite of the relative stability and precision of the frequency output of such quartz resonator controlled oscillators, frequency shifts and thus timing errors can occur when the resonator is subjected to acceleration (or gravity) caused stresses. These stresses are produced in the resonator as a result of interaction between the resonator crystal and its mounting or holding structure. Investigations have generally been unsuccessful in identifying effects, or whether there is any effect, of various parameters (crystal geometry, angle of cut, temperature, etc.) on acceleration sensitivity (see Filler et al "Further Studies on the Acceleration Sensitivity of Quartz Resonators", Proc. 37th Annual Symposium on Frequency Control, 1983, pp. 265-271; and Raymond L. Filler, "The Acceleration Sensitivity of Quartz Crystal Oscillators: A Review", Proc. 41st Annual Symposium on Frequency Control, May, 1987, pp. 398-408). Accordingly, there is a need for crystal oscillators and crystal resonators having low acceleration sensitivity.
Piezoelectric resonators, especially such devices as AT- and SC- cut quartz crystal resonators, are used in a number of applications in which they are subjected to acceleration, especially sinusoidal and random vibration, while operating. Acceleration causes the resonance frequency of a crystal resonator to change. For accelerations which are not too large, the frequency change is the scalar (dot) product of two spatial vector quantities, the acceleration sensitivity of the resonator and the acceleration (Raymond L. Filler, "The Acceleration Sensitivity of Quartz Crystal Oscillators: A Review", Proc. 41st Annual Symposium on Frequency Control, May 1987, pp. 398-408).
The acceleration sensitivity of a piezoelectric resonator depends upon two factors--the deformation produced by the acceleration and the mode shape. While the mathematical analysis is complex, the basic idea is simple and is described in "An Analysis of the Normal Acceleration Sensitivity of Contoured Quartz Resonators Rigidly Supported Along the Edges", H. F. Tiersten & D. V. Shick, Proceedings of the IEEE Ultrasonics Symposium, 1988, pp. 357-363. At each point in the resonator, acceleration-induced deformation alters the effective elastic stiffness of the resonator, thereby incrementally affecting the resonance frequency of each mode of vibration by an amount that depends upon the mode amplitude and sign and upon the amplitude and sign of the deformation at that point. While the mode amplitude is referred to here as if it were a single quantity, it should be recognized that the mode of vibration employed may have two or even more components, all of which may contribute to the total acceleration sensitivity. Similarly, the acceleration-induced deformation will, in general, have more than one component.
The total effect on the resonance frequency of a particular mode is the algebraic sum of the incremental effects taken over the entire volume of the resonator. Thus, the acceleration sensitivities of different modes of the same resonator are, in general, different from one another. For regions of the resonator where the amplitude of vibration is small, the incremental effect is small. Similarly, where the deformation is relatively small the effect will be relatively small. An extremely important aspect of the summation is that, due to symmetry, a high degree of cancellation takes place; that is, the sum of the positive increments is very nearly equal to the sum of the negative increments.
In a conventional thickness-mode quartz crystal unit, a suitably dimensioned and electroded platelet or wafer of quartz, commonly called a blank, is supported at two or more points on its periphery by metal ribbons or clips, which in turn are fastened to a header or base. Under acceleration, the body forces on the blank are balanced by reaction forces of the support structure. Thus, the support structure determines the acceleration-induced deformation of the blank. The mode shape of the resonator is determined by an energy-trapping mechanism. For a plano-plano resonator, the primary controls are the lateral dimensions of the electrodes, including the tabs, the electrode mass loading, and the piezoelectric loading. However, the mode shape, and hence the acceleration sensitivity, will also unavoidably be affected by point-to-point variations in the thickness of the blank (i.e. non-parallelism) or even of the electrode, as well as by material defects such as inclusions and etch channels. For contoured resonators, mode shape is primarily controlled by contour, but will also be affected to some degree by the electrodes and by material defects.
Because of fabrication limitations, variations from resonator to resonator in support geometry, in electrode dimensions, and in blank contour are unavoidable. Because the resonator acceleration sensitivity is the difference of two nearly equal quantities, small changes in the resonator, representing normal manufacturing tolerances, can cause large changes in resonator acceleration sensitivity. This is borne out by experience.
Consequently, it is desirable to have a means of adjusting, or trimming, the acceleration sensitivity in order to minimize its magnitude or the magnitude of one or more of its vector components. In principle, this may be accomplished by altering either the mode shape or the acceleration-induced deformation. The latter might be accomplished, say, by modifying the mounting structure. One method by which the mode shape may be altered is to add or remove mass from selected regions of the blank (U.S. Pat. No. 4,837,475 issued Jun. 6, 1989, EerNisse et al.